Numerical Analysis of Diffusion in Discrete Fracture Networks with Fractal Geometry by Using Pressure Transient Data

This article presents numerical analyses on diffusion trend for the fractured media with fractal properties by pressure transient data. The authors develop a discrete fracture model with random fracture pattern and a power-law length distribution, which has not been fully considered in the previous fractal modeling. From the model presented, the fractal dimension and conductivity index is determined, and the pressure behavior is analyzed for the range of length exponent (a) of power-law from 1 and 3.

Various fractal geometries are examined depending on the morphology of fractures. A single fractal characteristic is observed in the media dominated by long (a < 2) or small fractures (a > 3), and two distinct fractal dimensions in pertinently mixed system of long and small fractures (2 < a < 3). Also, pressure transient behaviors in the mixed system show their unique characteristics, corresponding to each fractal dimension respectively. It is shown that diffusion effect is relatively small in the early time influenced by a few long fractures, and becomes larger in the late time by long and small fractures.

Keywords:

• fractal diffusion
• fractured medium
• pressure transient behavior
• discrete fracture network
• fractal dimension

Acknowledgments

The authors gratefully acknowledge the financial support of the Korea Ministry of Science and Technology under the National Research Laboratory, contract M10104000042-01J000001700.